[GAP Forum] The order of Out(S4(8))

[Dmitrii Pasechnik]

Dear Forum,
it works for me (on OSX 10.6.8):

 *********   GAP, Version 4.6.4 of 04-May-2013 (free software, GPL)
 *  GAP  *   http://www.gap-system.org
 *********   Architecture: x86_64-apple-darwin10.8.0-gcc-default64
 Libs used:  gmp, readline
 Loading the library and packages ...
 Packages:   Alnuth 3.0.0, AutPGrp 1.5, CTblLib 1.2.2, FactInt 1.5.3,
GAPDoc 1.5.1, LAGUNA 3.6.3, Polycyclic 2.11
 Try '?help' for help. See also  '?copyright' and  '?authors'
gap> S:=PSp(4,8);
<permutation group of size 1056706560 with 2 generators>
gap> OrbitLength(S,1);
585
gap> NormalSubgroups(S);
[ Group(()), <permutation group of size 1056706560 with 2 generators> ]
gap> A:=AutomorphismGroup(S);
<group with 8 generators>
gap> Order(A)/Order(S);
6
gap> Size(A)/Size(S);
6


What version of GAP are you using, and on which OS/hardware?

On Tue, Feb 11, 2014 at 01:08:22PM +0700, Anvita wrote:
> Dear Forum,
> 
> According to the ATLAS, the simple group S4(8) has outer automorphism group
> of order 6,
> but the following calculation, if I am interpreting it correctly, seems to
> suggest that it has order 3.
> 
> Anvita
> 
> 
> gap> S:=PSp(4,8);
> <permutation group of size 1056706560 with 2 generators>
> gap> A:=AutomorphismGroup(S);
> <group with 4 generators>
> gap> Size(A)/Size(S);
> 3
> _______________________________________________